Saturn V Chemical Energy
How much energy would be released if a Saturn V rocket burned in the atmosphere?
Assume the liquid oxygen is equivalent to oxygen in the atmosphere; no net energy release. Ignore combustables and propellant in the LM, CM, SM, and escape tower. Airframe aluminum burns, but we won't include that combustion energy either. Let's hope for a 20% accurate guess.
Assume complete combustion; rockets typically run fuel-rich so that the exhaust has a lower molecular weight and higher speed. Rockets produce less energy (and more reactive rocket plumes) compared to the calculation below, when operated correctly.
The Saturn V rocket contains 770 kiloliters of RP-1 in the first stage, 984 kiloliters of LH₂ in the second stage and 253 kiloliters of LH₂ in the third stage. Assume a density of 0.07 for LH₂ and 0.81 for RP-1. That's 87 Mg of hydrogen and 620 Mg of RP-1.
Water has a standard enthalpy of formation of 285.83 kJ/mol, which I will interpret as 143 kJ per g of hydrogen.
According to Thermophysics Characterization of Kerosene Combustion page 13, the RP-1 heat of combustion is 10.278 kcal/g or 43 kJ/g.
Total energy is 143 kJ/g × 87 Mg + 43 kJ/g × 620 Mg or about 5.2e13 Joules.
A ton of explosive is 4.184e9 joules. So, the complete combustion of a Saturn V rocket in air is the energy equivalent of a 12 kT nuclear bomb.
These are estimates; I could only find the liters of fuel and typical fuel densities, not the actual fuel mass. The actual mass is needed for an accurate calculation.
Safety Risk Compared to a Launch Loop
For comparison, a 6000 kilometer length, 4.3 kg/m launch loop rotor moving at 12.5 km/s stores 2e15 J of kinetic energy. That is 480 kT nuclear bomb equivalent, or the energy equivalent of 40 burning Saturn V rockets.
Each Saturn V lofted a Command Module (CM), Service Module (SM), and Lunar Module (LM) to the moon; the mass of CM+SM+LM+contents was about 46 tonnes. With a full power supply, the launch loop example above can launch 400 tonnes per hour, or 40 Saturn V loads in 4.6 hours. If Saturn V rockets burn once per 200 missions, and the launch loop fails once every six months, the average energy release per tonne lifted is 1.3 tonnes explosive equivalent for the Saturn V, and 0.3 tonnes explosive equivalent for the launch loop.
Launch loops will operate mid-ocean, thousands of kilometers from populated land, and will have mechanisms for dumping most of the rotor into deep ocean (or deep space) in case of an accident. The Saturn V launched 80 kilometers from Orlando.
I hope that the launch loop will follow decades of development of energy storage loops, and will rarely fail after decades of use and repair. But people can be stupid and make mistakes; 1 failure per 2 million tonnes launched may be considered an acceptable risk by loop operators and investors. We accepted much higher risks to achieve Apollo's goals.